The area of a rectangle gets reduced by 26 m2, when
its length is increased by 2 m and its breadth is
decreased by 3 m. If we increase the length by 2 m and
breadth by 3 m, then the area increased by 46 m2. The
area of the rectangle is
Answers
Step-by-step explanation:
Given :-
The area of a rectangle gets reduced by 26 m2, when its length is increased by 2 m and its breadth is decreased by 3 m. If we increase the length by 2 m and breadth by 3 m, then the area increased by 46 m2.
To find :-
Find the area of the rectangle ?
Solution :-
Let the length of the rectangle be L m
Let the breadth of the rectangle be B m
Area of a rectangle = length× breadth
= LB sq.m ------(1)
If length is increased by 2 m then it becomes
(L+2) m
If breadth is decreased by 3 m then it becomes
(B-3) m
Area of the new rectangle
= (L+2)×(B-3) sq.m
=>( LB-3L+2B-6 ) sq.m -------(2)
Given that
The area of a rectangle gets reduced by 26 m^2, when its length is increased by 2 m and its breadth is decreased by 3 m.
=> LB -26 = LB-3L+2B-6
=> -26 = -3L+2B-6
=> 3L-2B = -6+26
=> 3L-2B = 20 -------------(3)
and
If length is increased by 2 m then it becomes
(L+2) m
If breadth is increased by 3 m then it becomes
(B+3) m
The area of the new rectangle
= (L+2)×(B+3)
=> LB +3L+2B+6 sq.m ---------(4)
Given that
If we increase the length by 2 m and breadth by 3 m, then the area increased by 46 m^2.
=> LB-46 = LB +3L+2B+6
=> LB-(LB +3L+2B+6) = 46
=> -3L-2B-6 = 46
=> -3L-2B = 46-6
=> -3L-2B = 40 ----------(5)
On adding (3) and (5) then
3L-2B = 20
-3L-2B = -40
(+)
__________
0-4B = -20
__________
=> -4B= -20
=>B = -20/-4
=> B = 5 m
On Substituting the value of B in (3)
=>3L-2(5) = 20
=> 3L- 10 = 20
=> 3L = 20+10
=> 3L = 30
=>L = 30/3
=>L = 10 m
So ,
Length = 10 m
Breadth = 5 m
Area of the rectangle = 10 m× 5 m =50 m^2
Answer:-
The area of the rectangle for the given problem is 50 m^2.
Check:-
Length = 10 m
Breadth = 5 m
The area of a rectangle gets reduced by 26 m^2, when its length is increased by 2 m and its breadth is decreased by 3 m.
=> (10+2)×(5-3)
=> (12)(2)
=> 24 m^2
Original area = 50 m^2
= 50= 24+26
=> 24 = 50-26
=> 26 m^2 decreased
and
If we increase the length by 2 m and breadth by 3 m, then the area increased by 46 m^2.
=> (10+2)×(5+3)
=>12×8
=> 96 m^2
Original area = 50 m^2
96 = 50+46
=> 46 m^2 increcreased
Verified the given relations in the given problem